CE 167 Midterm #1 Fall 2000 Prof. C.W. Ibbs Question #1 [15 Points] The amount of $600 per year is to be paid into an account over each of the next 4 years. The nominal interest rate is 15% per year. Determine the total amount the account will eventually contain under the following conditions: (a) Deposits are made at the beginning of the year with interest compounding yearly: NFV = [$600 (F/A, 15%, 4)](1+i) NFV = $600)1(1)1(iiin+−+NFV = $600)15.01(15.01)15.01(4+−+NFV = $344.45.43(b) Deposits at the end of the year with interest compounding yearly:NFV = [$600(F/A, 15%, 4)] This is the same as the Part (a), except you do not have to account for the extra year of interest NFV = $600−+15.01)15.01(4= $2996.03For Parts (a) & (b), 3 points were awarded for the correct usage of the formula, and 2 points for the correct answer. (c) $50 deposits are made at the end of each month with interest compounding monthly: Since i = 15% is a nominal yearly rate, you must find ieffective: ieffective= 11−+mmr= 11215.0112−+= 16.08% ieffective= 16.08% per year = 1.34% per month This part was worth 1 point A=$600 F=? Because the equations are set up so that payment are made at the end of the year, you have to account for the one extra year’s worth of interest made by making the deposit at the beginning of the year!A=$600 F=? 01230123
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